1. Field
The present disclosure is directed to a method and apparatus for equal energy codebooks for antenna arrays with mutual coupling.
2. Introduction
Presently, wireless communication devices communicate with other communication devices using wireless signals. Many wireless communication devices have multiple antennas that can transmit more focused signals to a receiving device using antenna beamforming. Multiple telecommunication standards define antenna precoder codebooks to support antenna beamforming and or multiple-input/multiple output (MIMO) transmission with feedback from a receiver in the receiving device. Precoders from the codebooks apply a vector of complex amplitudes to a transmitted signal to provide for the antenna beamforming Telecommunication standards that employ codebooks of precoders include the 3GPP HSPA and LTE standards and the IEEE 802.11 and 802.16 standards. In all of these standards, the precoders that are defined have the property that each precoding vector has equal L2 norm with the assumption that the precoders are applied to the antenna array in such a way that precoders having equal L2 norm yield antenna patterns with equal radiated power in the far field. Here the L2 norm (also known as the Euclidean norm) is defined as the square root of the sum of the square of the amplitudes so that for a vector x of length Mx=(x1 x2 . . . xM)T,the L2 or Euclidean norm is given by
      (                  ∑                  i          =          1                M            ⁢                                              x            i                                    2              )        1    2  
In each of the above telecommunication standards, precoders are used in combination with reference symbol transmissions so that the receiver can estimate and evaluate the quality of the channel that would result from application of each of the precoders. The receiver applies each of the precoders to the reference symbols in order to evaluate the channel quality. It then signals the index of the best precoder and the corresponding channel quality back to the transmitter. For some transmission modes, the precoder used for the data transmission is signaled from the transmitter to the receiver, and the receiver then applies the precoder to the channel estimates of the reference symbols in order to estimate the channel for the data symbols.
Implicit in the operation of these types of systems is the assumption that the precoders are applied in a manner such that the antenna pattern corresponding to each precoder has the same radiated power in the far field. The reason for this assumption is that it is the objective of the receiver to select the precoder which maximizes the channel quality, and thus the achievable data rate, for a given transmit power. In the case of a single user, this will maximize the transmission range of a fixed data rate, or alternatively, the achievable data rate at a fixed range. Alternatively, for multi-user systems, it is desirable to minimize the transmit power needed to achieve a given data rate for each user, as the transmit power for the target user is interference for all users other than the target user.
If there is no mutual coupling of the transmit array, then it will be true that antenna precoding vectors having equal L2 norm will yield antenna patterns with equal power (some assumptions are necessary; e.g., such as the source impedances are equal and the antenna elements have equal self-impedance). However, if the antennas are coupled, then the antenna patterns resulting from two precoders having the same L2 norm can differ in transmit power by several dB. The amount of this difference depends on multiple factors, including the mutual coupling coefficients, the type of sources used to drive the array, and the source impedances. Unfortunately, this difference results in a receiver making errors when evaluating channel quality from antenna arrays with mutual coupling.
Thus, there is a need for a method and apparatus for equal energy codebooks for antenna arrays with mutual coupling.